arXiv subjects

A. M. Kamchatnov

Publications and source records attributed to A. M. Kamchatnov.

At least 73 records · Page 4Linked to original sources

arXiv2013

Oblique breathers generated by a flow of two-component Bose-Einstein condensate past a polarized obstacle

We predict that oblique breathers can be generated by a flow of two-component Bose-Einstein condensate past a polarized obstacle which attracts one component of the condensate and repels the other one. The breather exists if intra-species interaction constants differ from the inter-species interaction constant and it corresponds to the nonlinear excitation of the so-called polarization mode with domination of the relative motion of the components. Approximate analytical theory is developed for the case of small-amplitude breathers that is in reasonable agreement with the exact numerical results.

cond-mat.quant-gas↗

arXiv2013

Nonlinear waves of polarization in two-component Bose-Einstein condensates

Waves with different symmetries exist in two-component Bose-Einstein condensates (BECs) whose dynamics is described by a system of coupled Gross-Pitaevskii (GP) equations. A first type of waves corresponds to excitations for which the motion of both components is locally in phase. In the second type of waves the two components have a counter-phase local motion. In the case of different values of inter- and intra-component interaction constants, the long wave-length behavior of these two modes corresponds to two types of sound with different velocities. In the limit of weak nonlinearity and small dispersion the first mode is described by the well-known Korteweg-de Vries (KdV) equation. We show that in the same limit the second mode can be described by the Gardner (modified KdV) equation, if the intra-component interaction constants have close enough values. This leads to a rich phenomenology of nonlinear excitations (solitons, kinks, algebraic solitons, breathers) which does not exist in the KdV description.

cond-mat.quant-gas↗

arXiv2013

Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation

Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg--de Vries (eKdV), or Gardner, equation. We consider both possible signs for the cubic nonlinear term in the Gardner equation corresponding to different fluid density stratification profiles. We identify the range of the input parameters: the oncoming flow speed (the Froude number) and the topographic amplitude, for which the obstacle supports a stationary localised hydraulic transition from the subcritical flow upstream to the supercritical flow downstream. Such a localised transcritical flow is resolved back into the equilibrium flow state away from the obstacle with the aid of unsteady coherent nonlinear wave structures propagating upstream and downstream. Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modeled by the forced KdV equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including solibores, rarefaction waves, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. The predictions of the developed analytic construction are confirmed by direct numerical simulations of the forced Gardner equation for a broad range of input parameters.

nlin.PS↗

arXiv2013

Undular bore theory for the Gardner equation

We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg--de Vries, equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation, when effects of higher order nonlinearity become important. Using a reduced version of the finite-gap integration method we derive the Gardner-Whitham modulation system in a Riemann invariant form and show that it can be mapped onto the well-known modulation system for the Korteweg--de Vries equation. The transformation between the two counterpart modulation systems is, however, not invertible. As a result, the study of the resolution of an initial discontinuity for the Gardner equation reveals a rich phenomenology of solutions which, along with the KdV type simple undular bores, include nonlinear trigonometric bores, solibores, rarefaction waves and composite solutions representing various combinations of the above structures. We construct full parametric maps of such solutions for both signs of the cubic nonlinear term in the Gardner equation. Our classification is supported by numerical simulations.

nlin.PS↗

arXiv2012

Wave pattern induced by a localized obstacle in the flow of a one-dimensional polariton condensate

Motivated by recent experiments on generation of wave patterns by a polariton condensate incident on a localized obstacle, we study the characteristics of such flows under the condition that irreversible processes play a crucial role in the system. The dynamics of a non-resonantly pumped polariton condensate in a quasi-one-dimensional quantum wire is modeled by a Gross-Pitaevskii equation with additional phenomenological terms accounting for the dissipation and pumping processes. The response of the condensate flow to an external potential describing a localized obstacle is considered in the weak-perturbation limit and also in the nonlinear regime. The transition from a viscous drag to a regime of wave resistance is identified and studied in detail.

cond-mat.quant-gas↗

arXiv2012

Generation of dispersive shock waves by the flow of a Bose-Einstein condensate past a narrow obstacle

We study the flow of a quasi-one-dimensional Bose-Einstein condensate incident onto a narrow obstacle. We consider a configuration in which a dispersive shock is formed and propagates upstream away from the obstacle while the downstream flow reaches a supersonic velocity, generating a sonic horizon. Conditions for obtaining this regime are explicitly derived and the accuracy of our analytical results is confirmed by numerical simulations.

cond-mat.quant-gas↗

arXiv2011

Oblique solitons in the flow of polariton condensate past an obstacle

Formation of oblique solitons by a flow of polariton condensate past an obstacle is considered. The flow is non-uniform due to a finite life-time of polaritons what changes drastically the conditions of formation of oblique solitons compared with the atomic condensate case. The theory shows that the polariton solitons can be generated by a subsonic flow in agreement with the recent experiment [A. Amo {\it et al.}, Science, {\bf 332,} 1167 (2011)]. Geometric form of oblique solitons and other their parameters are calculated analytically and analytical results are confirmed by numerical simulations.

cond-mat.quant-gas↗

arXiv2011

Condition for convective instability of dark solitons

Simple derivation of the condition for the transition point from absolute instability of plane dark solitons to their convective instability is suggested. It is shown that unstable wave packet expands with velocity equal to the minimal group velocity of the disturbance waves propagating along a dark soliton. The growth rate of the length of dark solitons generated by the flow of Bose-Einstein condensate past an obstacle is estimated. Analytical theory is confirmed by the results of numerical simulations.

cond-mat.quant-gas↗

arXiv2010

Development of instability of dark solitons generated by a flow of Bose-Einstein condensate past a concave corner

The stability of dark solitons generated by a supersonic flow of a Bose-Einstein condensate past a concave corner (or a wedge) is studied. It is shown that solitons in the dispersive shock wave generated at the initial moment of time demonstrate a snake instability during their evolution to stationary curved solitons. Time of decay of soliton to vortices agrees very well with analytical estimates of the instability growth rate.

nlin.PS↗

arXiv2010

Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics

Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solitons for general form of the nonlinear term in the generalized nonlinear Schroedinger or Gross-Pitaevskii equation. Analytical theory is illustrated by examples of dynamics of ring solitons in light beams propagating through a photorefractive medium and in non-uniform condensates confined in axially symmetric traps. Analytical results agree very well with the results of our numerical simulations.

nlin.PS↗

arXiv2010

Kinetic equation for a soliton gas and its hydrodynamic reductions

We introduce and study a new class of kinetic equations, which arise in the description of nonequilibrium macroscopic dynamics of soliton gases with elastic collisions between solitons. These equations represent nonlinear integro-differential systems and have a novel structure, which we investigate by studying in detail the class of $N$-component `cold-gas' hydrodynamic reductions. We prove that these reductions represent integrable linearly degenerate hydrodynamic type systems for arbitrary $N$ which is a strong evidence in favour of integrability of the full kinetic equation. We derive compact explicit representations for the Riemann invariants and characteristic velocities of the hydrodynamic reductions in terms of the `cold-gas' component densities and construct a number of exact solutions having special properties (quasi-periodic, self-similar). Hydrodynamic symmetries are then derived and investigated. The obtained results shed the light on the structure of a continuum limit for a large class of integrable systems of hydrodynamic type and are also relevant to the description of turbulent motion in conservative compressible flows.

nlin.SI↗

arXiv2009

Dark soliton oscillations in Bose-Einstein condensates with multi-body interactions

We consider the dynamics of dark matter solitons moving through non-uniform cigar-shaped Bose-Einstein condensates described by the mean field Gross-Pitaevskii equation with generalized nonlinearities, in the case when the condition for the modulation stability of the Bose-Einstein condensate is fulfilled. The analytical expression for the frequency of the oscillations of a deep dark soliton is derived for nonlinearities which are arbitrary functions of the density, while specific results are discussed for the physically relevant case of a cubic-quintic nonlinearity modeling two- and three-body interactions, respectively. In contrast to the cubic Gross-Pitaevskii equation for which the frequencies of the oscillations are known to be independent of background density and interaction strengths, we find that in the presence of a cubic-quintic nonlinearity an explicit dependence of the oscillations frequency on the above quantities appears. This dependence gives rise to the possibility of measuring these quantities directly from the dark soliton dynamics, or to manage the oscillation via the changes of the scattering lengths by means of Feshbach resonance. A comparison between analytical results and direct numerical simulations of the cubic-quintic Gross-Pitaevskii equation shows good agreement which confirms the validity of our approach.

cond-mat.quant-gas↗

arXiv2009

Two-dimensional supersonic nonlinear Schrödinger flow past an extended obstacle

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional defocusing nonlinear Schrödinger (NLS) equation. This problem is of fundamental importance as a dispersive analogue of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched $x$-coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half-planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear "ship wave" pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.

nlin.PS↗

arXiv2009

Transcritical flow of a Bose-Einstein condensate through a penetrable barrier

The problem of the transcritical flow of a Bose-Einstein condensate through a wide repulsive penetrable barrier is studied analytically using the combination of the localized "hydraulic" solution of the 1D Gross-Pitaevskii equation and the solutions of the Whitham modulation equations describing the resolution of the upstream and downstream discontinuities through dispersive shocks. It is shown that within the physically reasonable range of parameters the downstream dispersive shock is attached to the barrier and effectively represents the train of very slow dark solitons, which can be observed in experiments. The rate of the soliton emission, the amplitudes of the solitons in the train and the drag force are determined in terms of the BEC oncoming flow velocity and the strength of the potential barrier. A good agreement with direct numerical solutions is demonstrated. Connection with recent experiments is discussed.

cond-mat.other↗

arXiv2009

Stationary wave patterns generated by an impurity moving with supersonic velocity through a Bose-Einstein condensate

Formation of stationary 3D wave patterns generated by a small point-like impurity moving through a Bose-Einstein condensate with supersonic velocity is studied. Asymptotic formulae for a stationary far-field density distribution are obtained. Comparison with three-dimensional numerical simulations demonstrates that these formulae are accurate enough already at distances from the obstacle equal to a few wavelengths.

cond-mat.other↗

arXiv2008

Stabilization of Solitons Generated by a Supersonic Flow of Bose-Einstein Condensate Past an Obstacle

Stability of dark solitons generated by a supersonic flow of Bose-Einstein condensate past an obstacle is investigated. It is shown that in the reference frame attached to the obstacle a transition occurs at some critical value of the flow velocity from absolute instability of dark solitons to their convective instability. This leads to decay of disturbances of solitons at fixed distance from the obstacle and formation of effectively stable dark solitons. This phenomenon explains surprising stability of the flow picture that has been observed in numerical simulations.

cond-mat.other↗

arXiv2008

Wave patterns generated by a supersonic moving body in a binary Bose-Einstein condensate

Generation of wave structures by a two-dimensional object (laser beam) moving in a two-dimensional two-component Bose-Einstein condensate with a velocity greater than both sound velocities of the mixture is studied by means of analytical methods and systematic simulations of the coupled Gross-Pitaevskii equations. The wave pattern features three regions separated by two Mach cones. Two branches of linear patterns similar to the so-called "ship waves" are located outside the corresponding Mach cones, and oblique dark solitons are found inside the wider cone. An analytical theory is developed for the linear patterns. A particular dark-soliton solution is also obtained, its stability is investigated, and two unstable modes of transverse perturbations are identified. It is shown that, for a sufficiently large flow velocity, this instability has a convective character in the reference frame attached to the moving body, which makes the dark soliton effectively stable. The analytical findings are corroborated by numerical simulations.

cond-mat.other↗

arXiv2008

Matter sound waves in two-component Bose-Einstein condensates

The creation and propagation of sound waves in two-component Bose-Einstein condensates (BEC) are investigated and a new method of wave generation in binary BEC mixtures is proposed. The method is based on a fast change of the inter-species interaction constant and is illustrated for two experimental settings: a drop-like condensate immersed into a second large repulsive condensate, and a binary mixture of two homogeneous repulsive BEC's. A mathematical model based on the linearized coupled Gross-Pitaevskii equations is developed and explicit formulae for the space and time dependence of sound waves are provided. Comparison of the analytical and numerical results shows excellent agreement, confirming the validity of the proposed approach.

cond-mat.other↗